The present invention relates to the technique for finding a process tolerance in a semiconductor manufacturing process and to a method for calculating a process tolerance for finding a relation of a light exposure amount and focal point position corresponding to an allowable dimension value of a finished pattern formed from a resist pattern by lithography or from a pattern etched after a lithography.
Recently, attempts have been made to further extend a resolution limit to a finer dimension in the photolithography technique with the use of a new light exposure device technique, masking technique and resist technique. In order to quantity-produce an LSI with a pattern of a line width near such a finer-resolution limit, it is necessary to provide a process tolerance of over a given level.
Since, for example, the thickness of a resist film varies at a wafer surface area and in those coating devices, there occurs a variation in a proper amount of light with which a pattern is finished to a desired dimension. Further, there occurs a variation in focal point position resulting from the inaccuracy of the focal point positions the aberration of lenses, etc., in a light exposure device. And a variation in an amount of light exposure leads to an error in dimension of a finished resist pattern and a variation in the focal point position causes a variation in the shape of the finished resist pattern.
In the actual photolithography, a fluctuation in the amount of light exposure and in the focal point position exerts a greater influence over the finished dimension or configuration of the resin pattern. As the resolution becomes nearer to its limit, the process tolerance obtained is lowered and the resin pattern suffers a relative influence. In order to quantity-produce LSIs with a pattern of a line width near the resolution limit, it is necessary to provide a process tolerance of over a given value and hence to strictly find the process tolerance for evaluation.
By examining any adverse effects upon the dimension of the resist pattern caused by a variation in the amount of light exposure and focal point position it is possible to give judgment on whether or not LSIs can be quantity-produced with the light exposure method and resist process adopted. Further, it is also possible to determine the upper limit on the fluctuation in the amount of light exposure and focal point position.
In order to find the process tolerance on the variation in the focal point position and amount of light exposure, the dependence of the dimension (line width) of the resist pattern upon the focal point position and amount of light exposure is found. Based on this it is possible to find the range of the focal point position and amount of light exposure in terms of the dimension of the resist pattern, that is, the range in which semiconductor devices operate normally. This is called, here, a process tolerance allowing this dimensional range.
The process tolerance can be represented by two curves corresponding to the upper and lower limit line widths of an allowable range in terms of a desired pattern dimension in a graph with the defocusing plotted in a vertical direction and the amount of light exposure in a horizontal direction. Such a line diagram is referred to as an ED-tree.
A logical development of such a process tolerance is discussed in detail in a document (B. J. Lin, "Partially Coherent Imaging in Two Dimensions and Theoretical Limits of Projection Printing in Microfabrication", IEEE Tran. Electron Devices, vol. ED-27, pp.931 (1980)).
In order to accurately know the above-mentioned process tolerance, it is necessary to both include a range of a focal point position and that of an amount of light exposure capable of measuring a resist pattern's dimension and take a larger value than this range.
That is, if the resist pattern's line width corresponding to the measurable range of defocusing and amount of light exposure fails to reach the lower and upper limits of the allowable range, it is not possible to find corresponding values from the ED-tree. In other words, in the method for finding an ED-tree from a result of the dependence of the focal point position and of the amount of light exposure, it is not possible to obtain a right result in the case where a desired ED-tree falls outside the measured range of the focal point position or the amount of light exposure.
It may be considered that, for those outside the range, the procedure is taken whereby a result of measurement is predicted through the curve approximation. Even in this case, a right result has not been acquired in the case where there occurs a greater variation among results of measurement conducted.
In order to find the ED-tree for instance, measurement is made by varying the focal point position with an amount of light exposure given and, based on a measured resist pattern dimension, the dependence of the resist pattern dimension upon the focal point position is found from a regression analysis (curve approximation) in which case, if there is a greater variation among the results of measurement, it will be followed that an inaccurate approximation result is obtained at a greater defocusing area.
FIG. 6 shows the dependence of the resist's line width upon the defocusing in the case of using a positive type resist. Since the positive type resist is used, even if any resist's line width is taken at any defocusing area, the resist's line width should be made smaller when a greater amount of light exposure is involved than when a smaller amount of light exposure is involved, so that there sometimes occur crosses (points C in FIG. 6) though being dependent upon the results of measurement.
This is considered to be caused by errors of measurement at those areas where a greater defocusing occurs. If any curve approximation is done at those areas where greater errors of measurement occur, it follows that such errors are increased as greater ones.